1. Circles and Arcs

2. General Vocabulary:
CIRCLE: the set of all points equidistant from a given point called the CENTER
RADIUS: a segment that has one point at the center and the other endpoint on the circle
DIAMETER: a segment that contains the center of a circle and has both endpoints on the circle

3. Central Angles
CENTRAL ANGLE: an angle whose vertex is on the center of the circle
Name all the central angles above. B A C O D

4. Arcs ARC: part of a circle SEMICIRCLE: half of a circle
MINOR ARC: smaller than a semicircle
MAJOR ARC: bigger than a semicircle
ADJACENT ARCS: arcs of the same circle that have exactly one point in common

5. Arcs B A C O D Name all the semicircles above.
Name all the minor arcs above.
Name all the major arcs above.
Name all the adjacent arcs above. A C O D

6. Arcs B A C O D Arc Addition Postulate:
The measure of the arc formed by two adjacent arcs
is the sum of the measures of the two arcs.
m ABC = m AB + m BC A C O D

7. Circumference and Arc Length
Circumference of a Circle: 2πr or πd
Arc Length:
The length of an arc of a circle is the product of the circumference and (degree measure of arc/360)
length of AB = m AB * 2πr
360 B r O A

8. Circumference and Arc Length
Arc Length: length of AB = m AB * 2πr
360
Length of AB = 140 * 2π5
Length of AB = 12.21 B C
1400 5 O A D

9. Circumference and Arc Length
Arc Length: length of AB = m AB * 2πr
360
Length of AB = B C 12 O A
500 D

10. Misc Congruent circles have congruent radii
Concentric circles lie in the same plane and have the same center
Congruent arcs have the same measure AND are in the same circle or congruent circles